advertisement

Algebra 1P: Standard 3: Name __________________________ Solving Absolute Value Equations Homework Worksheet # 1 Things to know: I know… The absolute value of a number means its distance from zero. To find the distance between 2 numbers, x and b, I calculate the absolute value of their difference: the distance from x to b or from b to x = | x – b | = | b – x |. If the | x – b | = c, then x is c units from b in either direction. Draw graphs for the following equations: 1. | x | = 3 -6 -4 -2 0 2 4 6 x = _____ or x = ______ 4. | x – 1 | = 3 -6 -4 -2 3. | x – 0 | = 5 2. | x | = 2 0 -6 -4 -2 0 2 4 6 x = _____ or x = ______ 5. | x – 4 | = 2 2 4 6 x = _____ or x = ______ 7. | x + 2 | = 3 x = _____ or x = ______ 10. | x – 4 | = 1 x = _____ or x = ______ -6 -4 -2 0 -6 -4 -2 0 2 4 6 x = _____ or x = ______ 6. | x + 1 | = 5 2 4 6 x = _____ or x = ______ 8. | x – 5 | = 0 x = _____ or x = ______ 11. | x + 4 | = 2 x = _____ or x = ______ -6 -4 -2 0 2 4 6 x = _____ or x = ______ 9. | x + 3 | = 4 x = _____ or x = ______ 12. | x + 1 | = -5 x = _____ or x = ______ 13. Graph the solutions for x if |x – b| = c. Which value is plotted first? _______ Which value tells the distance? __________ Label the solution points in terms of b and c. x b What can x equal? x = ___________ or x = ____________ Algebra 1P: Standard 3: Name __________________________ Solving Absolute Value Equations Homework: Worksheet # 2 Things to know: I know… The absolute value of a number means its distance from zero. To find the distance between 2 numbers, x and b, I calculate the absolute value of their difference: the distance from x to b or from b to x = | x – b | = | b – x |. EX: If the | x – b | < 6, then x is less than 6 units from b in either direction. If the | x – b | > 6 number, then x is greater than 6 units from b in either direction. Draw graphs for the following inequalities; then write the algebraic solutions: 1. | x | > 2 x < _____ or x > ______ 4. | x – 1 | < 3 _____ < x < ______ ____________________ 6. | x + 1 | < 4 x < _____ or x > ______ _____ < x < ______ 8. | x – 5 | < 0 ____________________ 10. | x – 4 | < -1 x < _____ or x > ______ 5. | x – 4 | > 2 _____ < x < ______ 7. | x + 2 | > 3 3. | x – 0 | > 4 2. | x | < 5 9. | x + 3 | > 0 ____________________ ____________________ 11. | x + 4 | > 2 ____________________ 12. | x + 1 | < 5 ___________________ 13. Graph the solutions for x if |x – b| < c. Which value (b or c) is plotted first? ____________Which value tells the distance? ___________ Are the possible x values in one continuous region or two separate pieces of the graph? ____________ What can x equal? _______________________ x 14. Graph the solutions for x if |x – b| > c. Is the set of possible x values one continuous region or two separate pieces of the graph? ____________ x What can x equal? _______________________ Algebra 1P: Standard 3: Name __________________________ Solving Absolute Value Equations Homework: Worksheet # 3 Example: | 5 – 2x | < 3 2x -6 -4 -2 0 x 0 2 1 5 5/2 8 4 Graph 2x: all points 3 or less units away from 5; 5-3 = 2 and 5+3 =8 Solution for 2x: All points between and including 2 and 8. Graph x: divide the solution for 2x by 2: 2/2 = 1 and 8/2 = 4. Solution for x: All points between 1 and 4, inclusive. | 5 – 2x | < 3 5 – 3 < 2x < 5 + 3 2 < 2x < 8 1< x <4 Solve the following absolute value inequalities first for ax and then for x. Draw the graph and write the algebraic solution statement for each of the following problems: 1. | 3x | > 2 2. | 2x | < 5 3. | 4x – 0 | > 8 3x 4x 2x x x x 3x < _____ or 3x > ______ _____ < 2x < ______ 4x < _____ or 4x > _____ x < _____ or x > ______ _____ < x < ______ x < _____ or x > ______ 4. | 2x – 1 | > 3 5. | 5x – 4 | < 2 6. | 4 – 3x | < 4 2x 5x 3x x x x 2x < _____ or 2x > ______ _____ < 5x < ______ _____ < 3x < _____ x < _____ or x > ______ _____ < x < ______ _____ < x < _____ 8. | 7 – 5x | < 3 7. | 6x + 2 | > 4 6x x 9. | 2x + 3 | > 5 5x 2x x x 6x: __________________ 5x: __________________ 2x: __________________ x: _________________ x: __________________ x: ___________________